First Day

Step 1: Punch a Tree

The first thing you'll need is wood. Approach a tree, and punch it (by holding down the left mouse button) until a chunk of wood breaks off.

You will be rewarded with an achievement!

Repeat until you have collected all the wood from the tree. You should have 4 or 5 blocks of wood.

Step 2. Get Crafting

The next step is to craft some of the things you'll need. The first thing to do is to convert the wood you just harvested into wooden planks.
Press 'E' to open your inventory screen.

Practise moving items around on your inventory screen. Left-click with the mouse to pick up your whole stack of wood. Right-click on any square to place a single item, or left-click to drop the whole stack.
Pick up the wood and place it in the crafting area on your inventory screen.

Convert a few blocks of wood to Wooden Planks.

Make a Crafting Table

Now use 4 Wooden Planks to create a Crafting Table:

Place the Crafting Table in your Toolbar, and press 'E' to close your inventory. Select the Crafting Table by pressing keys 1&endash;9 (or use a scroll wheel) and right-click to place it on the floor.

Right click on the table, and you'll see another screen with your inventory and a crafting area; this time the crafting area is a 3x3 square.

Make Your First Tool

Place two planks on the Crafting Table, one above the other, to make some sticks:

Next, use sticks and planks to make a Wooden Pickaxe:

This is your first tool; you can use it to dig, chop down trees or kill things. You could make other wooden tools at this point, but there's not much point since you want to move on to stone tools and better as soon as possible.
Chop down another tree, this time using your pickaxe.
You can break down your crafting table to bring it with you, by whacking it with your pickaxe. Or you can build a new one when you need it.

Step 3. Build a home

With your pickaxe, start digging a new home, The doorway should be 2 blocks high and 1 block wide, opening up into a larger space inside.

Don't do too much at first: as soon as you have a bit of space inside, you will want to do some more crafting.
Place a Crafting Table inside your new home.

Make Torches

You will want to make some torches to light up your home. Did you find some coal? If so that's lucky. Make torches with coal and sticks!

(You can do this either on a Crafting Table or in your Inventory)

If you didn't find coal, you will need to make Charcoal. Whilst digging, did you get blocks of Cobblestone? If not, dig some more stone until you have 8.
Go to your crafting table, and make a furnace:

Place the furnace somewhere convenient. Now right-click on it and you will see this interface:

Place 3 blocks of Wood in the top section ("Ingredients") and 2 Wooden Planks below (in the "Fuel" slot).

You will see flames, and the Wood will be turned into Charcoal. Use the Charcoal to make torches, exactly as described above.

Light Up Your Room

Holding your torches, right-click to place them on your floor or wall. Make sure your home is well-lit at all times - no corner should be more than 6 blocks from a torch.

Shut The Door!

The last thing to accomplish is building a door to keep monsters out. You should still have 6 wooden planks. Lay them out on your crafting table like so:

Place the door by right clicking on the floor in the doorway and your house is now a safe refuge! You will survive the night, and you have light by which to get started on some home improvements.

 

Step 4. Home Improvements

You might want to use any remaining daylight to collect more wood, coal, or any other nearby resources.
When it's dark, you can see about expanding your new home, squaring things off and maybe building some new rooms.

Upgrade Your Tools

You will probably want to use your Crafting Table to make better tools using Cobblestone instead of Wood Planks.

Make Windows

You might want windows to see the outside world in the morning.
Did you find some sand? You might want to make a window. Use your furnace to make sand into glass; you can read more about furnaces and efficient use of fuel first if you like.
You can use a glass block as a window, or make proper window-panes:

If you don't have any glass, a single block hole can still be used as a window. It's too small for monsters to get through, but a skeleton might shoot arrows through if you are unlucky.

Tip: Make sure you light your home well by placing plenty of torches, otherwise monsters may appear! A good rule of thumb is that no square of your floor should be more than 6 blocks away from a torch. More on lighting.

Did you kill some sheep? If so, you might want to make a bed and sleep through the night.

Storage

You will probably want some storage chests to put your stuff in as you collect more:

Two chests placed side by side create a larger, double chest.

Source: http://www.minecraft101.net